We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of m^2=n^2+nl+l^2.
Publications
Pages
Thursday, 6 September, 2018
arXiv:1809.02037
Tuesday, 4 September, 2018
Let c_n = c_n(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice \mathbb{Z}^d. Let \mu = \lim_n c_n^{1/n} denote the...
arXiv:1809.00760
Monday, 3 September, 2018
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a...
arXiv:1809.00516
Wednesday, 29 August, 2018
Given a real function f on an interval [a,b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f,f′ and f...
arXiv:1808.09690
Tuesday, 28 August, 2018
We prove a local law for the adjacency matrix of the Erd\H{o}s-R\'enyi graph G(N,p) in the supercritical regime pN \geq C\log N where G(N,p) has with high probability no isolated vertices. In...
arXiv:1808.09437
Tuesday, 28 August, 2018
The celebrated Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory describes the universal correlations of eigenvalues on the microscopic scale, i.e....
arXiv:1808.09436
Tuesday, 28 August, 2018
We study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q>4. Their existence is closely related to the weak first-order phase transition and walking RG...
arXiv:1808.04380
Thursday, 23 August, 2018
During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects....
arXiv:1808.09282
Wednesday, 22 August, 2018
Given a graph G and a bijection f : E(G)\rightarrow \{1, 2, \ldots,e(G)\}, we say that a trail/path in G is f-\emph{increasing} if the labels of consecutive edges of this trail/path form an...
arXiv:1808.07351
Tuesday, 21 August, 2018
For a compact Poisson-Lie group K, the homogeneous space K/T carries a family of symplectic forms\omega_\xi^s, where \xi \in \mathfrak{t}^*_+ is in the positive Weyl chamber and s \in \mathbb{R...
arXiv:1808.06975
Friday, 17 August, 2018
We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the limit...
arXiv:1808.05958
Friday, 17 August, 2018
We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the...
arXiv:1807.11512